Answer :

Certainly! Let's solve the inequality involving the given expression [tex]\(9x - 22\)[/tex].

### Step-by-Step Solution:

1. Write Down the Inequality:
We start with an inequality involving the given expression [tex]\((9x - 22) > 0\)[/tex].

2. Isolate [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we need to manipulate the inequality such that [tex]\(x\)[/tex] is on one side of the inequality symbol.

[tex]\(9x - 22 > 0\)[/tex]

3. Add 22 to Both Sides:
Add 22 to both sides of the inequality to start isolating [tex]\(x\)[/tex].

[tex]\(9x - 22 + 22 > 0 + 22\)[/tex]

This simplifies to:

[tex]\(9x > 22\)[/tex]

4. Divide Both Sides by 9:
To solve for [tex]\(x\)[/tex], divide both sides of the inequality by 9.

[tex]\(\frac{9x}{9} > \frac{22}{9}\)[/tex]

This simplifies to:

[tex]\(x > \frac{22}{9}\)[/tex]

5. Interpret the Inequality:
The solution to our inequality is [tex]\(x > \frac{22}{9}\)[/tex]. In interval notation, this is written as:

[tex]\(\left( \frac{22}{9}, \infty \right)\)[/tex]

### Conclusion:
The inequality we wrote and solved describes the set of possible values for [tex]\(x\)[/tex] such that [tex]\((9x - 22) > 0\)[/tex]. Therefore, the solution to the inequality is:

[tex]\[ x > \frac{22}{9} \][/tex]

In interval notation, this is:

[tex]\[ \left( \frac{22}{9}, \infty \right) \][/tex]